Asked by Rebekah Gonzalez on May 06, 2024
Verified
A competitive market is made up of 100 identical firms. Each firm has a short-run marginal cost function as follows:
MC = 5 + 0.5Q,
where Q represents units of output per unit of time. The firm's average variable cost curve intersects the marginal cost at a vertical distance of 10 above the horizontal axis. Determine the market short-run supply curve. Calculate the price that would make 2,000 units forthcoming per time period. Note the minimum price at which any quantity would be placed on the market.
Marginal Cost Function
A mathematical representation that describes how the cost of producing one additional unit of a good varies as the quantity of production changes.
Market Short-Run Supply
The total quantity of a good or service that producers are willing and able to sell at current prices in the short run, considering fixed and variable costs.
Units of Output
The individual items or quantities produced by a process or system.
- Comprehend the connection between marginal cost, average variable cost, fixed costs, and their consequences for short-run supply curves.
Verified Answer
Q = 2MC - 10.
Now add the 100 short-run supply curves together:
Q1 = 2MC - 10
Q2 = 2MC - 10
. . .
. . .
. . .
Q100 = 2MC - 10
__________________________ = 200MC - 1000
Now, solve for MC
MC = MC = 0.005ΣQ + 5 (above MC = 10)
At ΣQ = 2000, the price would be
P = MC = 0.005(2000) + 5 = $15 per unit.
The lowest point on the supply curve would be just above the intersection with the average variable cost curve (at 10 units above the horizontal axis).
Learning Objectives
- Comprehend the connection between marginal cost, average variable cost, fixed costs, and their consequences for short-run supply curves.
Related questions
The Table Below Provides Cost Information for Two Firms in ...
Three Hundred Firms Supply the Market for Paint ...
Suppose All Firms Have Constant Marginal Costs That Are the ...
Short-Run Supply Curves for Perfectly Competitive Firms Tend to Be ...
The Marginal Cost Curves of Six Firms in an Industry ...